CISMN: A Chaos-Integrated Synaptic-Memory Network with Multi-Compartment Chaotic Dynamics for Robust Nonlinear Regression

CISMN: A Chaos-Integrated Synaptic-Memory Network with Multi-Compartment Chaotic Dynamics for Robust Nonlinear Regression

Modeling complex, non-stationary dynamics remains challenging for deterministic neural networks. We present the Chaos-Integrated Synaptic-Memory Network (CISMN), which embeds controlled chaos across four modules—Chaotic Memory Cells, Chaotic Plasticity Layers, Chaotic Synapse Layers, and a Chaotic A...

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Bibliographic Details
Main Authors: Yaser Shahbazi, Mohsen Mokhtari Kashavar, Abbas Ghaffari, Mohammad Fotouhi, Siamak Pedrammehr
Format: Article
Language:English
Published: MDPI AG 2025-05-01
Series:Mathematics
Subjects:
Chaos-Integrated Synaptic-Memory Network (CISMN)
chaos theory
artificial neural networks
dynamic learning
machine learning
complex systems
Online Access:https://www.mdpi.com/2227-7390/13/9/1513
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Summary:Modeling complex, non-stationary dynamics remains challenging for deterministic neural networks. We present the Chaos-Integrated Synaptic-Memory Network (CISMN), which embeds controlled chaos across four modules—Chaotic Memory Cells, Chaotic Plasticity Layers, Chaotic Synapse Layers, and a Chaotic Attention Mechanism—supplemented by a logistic-map learning-rate schedule. Rigorous stability analyses (Lyapunov exponents, boundedness proofs) and gradient-preservation guarantees underpin our design. In experiments, CISMN-1 on a synthetic acoustical regression dataset (541 samples, 22 features) achieved R<sup>2</sup> = 0.791 and RMSE = 0.059, outpacing physics-informed and attention-augmented baselines. CISMN-4 on the PMLB sonar benchmark (208 samples, 60 bands) attained R<sup>2</sup> = 0.424 and RMSE = 0.380, surpassing LSTM, memristive, and reservoir models. Across seven standard regression tasks with 5-fold cross-validation, CISMN led on diabetes (R<sup>2</sup> = 0.483 ± 0.073) and excelled in high-dimensional, low-sample regimes. Ablations reveal a scalability–efficiency trade-off: lightweight variants train in <10 s with >95% peak accuracy, while deeper configurations yield marginal gains. CISMN sustains gradient norms (~2300) versus LSTM collapse (<3), and fixed-seed protocols ensure <1.2% MAE variation. Interpretability remains challenging (feature-attribution entropy ≈ 2.58 bits), motivating future hybrid explanation methods. CISMN recasts chaos as a computational asset for robust, generalizable modeling across scientific, financial, and engineering domains.
ISSN:2227-7390

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